\begin{abstract}
Atomistic simulations on the silicon carbide precipitation in bulk silicon employing both, classical potential and first-principles methods are presented.
For the quantum-mechanical treatment basic processes assumed in the precipitation process are mapped to feasible systems of small size.
-Results of the accurate first-principles calculations on the carbon diffusion in silicon are compared to results of classical potential simulations revealing significant limitations of the latter method.
+Results of the accurate first-principles calculations on defects and carbon diffusion in silicon are compared to results of classical potential simulations revealing significant limitations of the latter method.
An approach to work around this problem is proposed.
Finally results of the classical potential molecular dynamics simulations of large systems are discussed.
\end{abstract}
-\keywords{point defects, migration, interstitials, first-principles calculations, classical potentials, ... more ...}
-\pacs{61.72.uf,66.30.-h,31.15.A-,34.20.Cf, ... more ...}
+\keywords{point defects, migration, interstitials, first-principles calculations, classical potentials, molecular dynamics, silicon carbide, ion implantation}
+\pacs{61.72.J-,61.72.-y,66.30.Lw,66.30.-h,31.15.A-,31.15.xv,34.20.Cf,61.72.uf}
\maketitle
% --------------------------------------------------------------------------------
While in CVD and MBE surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
However, in another IBS study Nejim et~al.\cite{nejim95} propose a topotactic transformation that is likewise based on the formation of substitutional C.
The formation of substitutional C, however, is accompanied by Si self-interstitial atoms that previously occupied the lattice sites and concurrently by a reduction of volume due to the lower lattice constant of SiC compared to Si.
-Both processes are believed to compensate each other.
+Both processes are believed to compensate one another.
Solving this controversy and understanding the effective underlying processes will enable significant technological progress in 3C-SiC thin film formation driving the superior polytype for potential applications in high-performance electronic device production.
It will likewise offer perspectives for processes that rely upon prevention of precipitation events, e.g. the fabrication of strained pseudomorphic Si$_{1-y}$C$_y$ heterostructures\cite{strane96,laveant2002}.
Atomistic simulations offer a powerful tool to study materials on a microscopic level providing detailed insight not accessible by experiment.
-In particular, molecular dynamics (MD) constitutes a suitable technique to investigate the dynamical and structural properties of some material.
-Modelling the processes mentioned above requires the simulation of a large amount of atoms ($\approx 10^5-10^6$), which inevitably dictates the atomic interaction to be described by computationally efficient classical potentials.
-These are, however, less accurate compared to quantum-mechanical methods and their applicability for the description of the physical problem has to be verified first.
+In particular, molecular dynamics (MD) constitutes a suitable technique to investigate their dynamical and structural properties.
+Modelling the processes mentioned above requires the simulation of a large number of atoms ($\approx 10^5-10^6$), which inevitably dictates the atomic interaction to be described by computationally efficient classical potentials.
+These are, however, less accurate compared to quantum-mechanical methods and their applicability for the description of the physical problem has to be verified beforehand.
The most common empirical potentials for covalent systems are the Stillinger-Weber\cite{stillinger85}, Brenner\cite{brenner90}, Tersoff\cite{tersoff_si3} and environment-dependent interatomic potential\cite{bazant96,bazant97,justo98}.
These potentials are assumed to be reliable for large-scale simulations\cite{balamane92,huang95,godet03} on specific problems under investigation providing insight into phenomena that are otherwise not accessible by experimental or first-principles methods.
Until recently\cite{lucas10}, a parametrization to describe the C-Si multicomponent system within the mentioned interaction models did only exist for the Tersoff\cite{tersoff_m} and related potentials, e.g. the one by Gao and Weber\cite{gao02} as well as the one by Erhart and Albe\cite{albe_sic_pot}.
In a combined ab initio and empirical potential study it was shown that the Tersoff potential properly describes binding energies of combinations of C defects in Si\cite{mattoni2002}.
However, investigations of brittleness in covalent materials\cite{mattoni2007} identified the short range character of these potentials to be responsible for overestimated forces necessary to snap the bond of two next neighbored atoms.
In a previous study\cite{zirkelbach10a} we approved explicitly the influence on the migration barrier for C diffusion in Si.
-Using the Erhart/Albe (EA) potential\cite{albe_sic_pot} an overestimated barrier height compared to ab initio calculations and experiment is obtained.
+Using the Erhart/Albe (EA) potential\cite{albe_sic_pot}, an overestimated barrier height compared to ab initio calculations and experiment is obtained.
A proper description of C diffusion, however, is crucial for the problem under study.
In this work, a combined ab initio and empirical potential simulation study on the initially mentioned SiC precipitation mechanism has been performed.
Reproducing the SiC precipitation was attempted by the successive insertion of 6000 C atoms (the number necessary to form a 3C-SiC precipitate with a radius of $\approx 3.1$ nm) into the Si host, which has a size of 31 Si unit cells in each direction consisting of 238328 Si atoms.
At constant temperature 10 atoms were inserted at a time.
Three different regions within the total simulation volume were considered for a statistically distributed insertion of the C atoms: $V_1$ corresponding to the total simulation volume, $V_2$ corresponding to the size of the precipitate and $V_3$, which holds the necessary amount of Si atoms of the precipitate.
-After C insertion the simulation has been continued for \unit[100]{ps} and cooled down to \unit[20]{$^{\circ}$C} afterwards.
+After C insertion the simulation has been continued for \unit[100]{ps} and is cooled down to \unit[20]{$^{\circ}$C} afterwards.
A Tersoff-like bond order potential by Erhart and Albe (EA)\cite{albe_sic_pot} has been utilized, which accounts for nearest neighbor interactions only realized by a cut-off function dropping the interaction to zero in between the first and second next neighbor distance.
The potential was used as is, i.e. without any repulsive potential extension at short interatomic distances.
Constant pressure simulations are realized by the Berendsen barostat\cite{berendsen84} using a time constant of \unit[100]{fs} and a bulk modulus of \unit[100]{GPa} for Si.
This finding is in agreement with several theoretical\cite{burnard93,leary97,dal_pino93,capaz94} and experimental\cite{watkins76,song90} investigations.
Astonishingly EA and DFT predict almost equal formation energies.
There are, however, geometric differences with regard to the DB position within the tetrahedron spanned by the four next neighbored Si atoms, as already reported in a previous study\cite{zirkelbach10a}.
-Since the energetic description is considered more important than the structural description minor discrepancies of the latter are assumed non-problematic.
+Since the energetic description is considered more important than the structural description, minor discrepancies of the latter are assumed non-problematic.
The second most favorable configuration is the C$_{\text{i}}$ \hkl<1 1 0> DB followed by the C$_{\text{i}}$ bond-centered (BC) configuration.
For both configurations EA overestimates the energy of formation by approximately \unit[1]{eV} compared to DFT.
Thus, nearly the same difference in energy has been observed for these configurations in both methods.
Instead the tetrahedral defect configuration is favored.
This limitation is assumed to arise due to the cut-off.
In the tetrahedral configuration the second neighbors are only slightly more distant than the first neighbors, which creates the particular problem.
-Indeed an increase of the cut-off results in increased values of the formation energies\cite{albe_sic_pot}, which is most significant for the tetrahedral configuration.
+Indeed, an increase of the cut-off results in increased values of the formation energies\cite{albe_sic_pot}, which is most significant for the tetrahedral configuration.
The same issue has already been discussed by Tersoff\cite{tersoff90} with regard to the description of the tetrahedral C defect using his potential.
-While not completely rendering impossible further, more challenging, empirical potential studies on large systems, the artifact has to be taken into account in the following investigations of defect combinations.
+While not completely rendering impossible further, more challenging empirical potential studies on large systems, the artifact has to be taken into account in the following investigations of defect combinations.
%This artifact does not necessarily render impossible further challenging empirical potential studies on large systems.
%However, it has to be taken into account in the following investigations of defect combinations.
For a possible clarification of the controversial views on the participation of C$_{\text{s}}$ in the precipitation mechanism by classical potential simulations, test calculations need to ensure the proper description of the relative formation energies of combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ compared to C$_{\text{i}}$.
This is particularly important since the energy of formation of C$_{\text{s}}$ is drastically underestimated by the EA potential.
-A possible occurrence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which obviously is wrong.
+A possible occurrence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which is obviously wrong.
Since quantum-mechanical calculations reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground state configuration of Si$_{\text{i}}$ in Si it is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.
Empirical potentials, however, predict Si$_{\text{i}}$ T to be the energetically most favorable configuration.
Combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ T are energetically less favorable than the ground state C$_{\text{i}}$ \hkl<1 0 0> DB configuration.
With increasing separation distance the energies of formation decrease.
However, even for non-interacting defects, the energy of formation, which is then given by the sum of the formation energies of the separated defects (\unit[4.15]{eV}) is still higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB.
-Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a next neighbored C$_{\text{s}}$, which is the most favored configuration of C$_{\text{s}}$ and Si$_{\text{i}}$ according to quantum-mechanical calculations\cite{zirkelbach10b} likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T.
+Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a next neighbored C$_{\text{s}}$, which is the most favored configuration of C$_{\text{s}}$ and Si$_{\text{i}}$ according to quantum-mechanical calculations\cite{zirkelbach10b}, likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T.
This is attributed to an effective reduction in strain enabled by the respective combination.
Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential.
\label{subsection:cmob}
To accurately model the SiC precipitation, which involves the agglomeration of C, a proper description of the migration process of the C impurity is required.
-As shown in a previous study\cite{zirkelbach10a} quantum-mechanical results properly describe the C$_{\text{i}}$ \hkl<1 0 0> DB diffusion resulting in a migration barrier height of \unit[0.90]{eV} excellently matching experimental values of \unit[0.70-0.87]{eV}\cite{lindner06,tipping87,song90} and, for this reason, reinforcing the respective migration path as already proposed by Capaz et~al.\cite{capaz94}.
+As shown in a previous study\cite{zirkelbach10a}, quantum-mechanical results properly describe the C$_{\text{i}}$ \hkl<1 0 0> DB diffusion resulting in a migration barrier height of \unit[0.90]{eV}, excellently matching experimental values of \unit[0.70-0.87]{eV}\cite{lindner06,tipping87,song90} and, for this reason, reinforcing the respective migration path as already proposed by Capaz et~al.\cite{capaz94}.
During transition a C$_{\text{i}}$ \hkl[0 0 -1] DB migrates towards a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the next neighbored lattice site in \hkl[1 1 -1] direction.
However, it turned out that the description fails if the EA potential is used, which overestimates the migration barrier (\unit[2.2]{eV}) by a factor of 2.4.
In addition a different diffusion path is found to exhibit the lowest migration barrier.
A C$_{\text{i}}$ \hkl[0 0 -1] DB turns into the \hkl[0 0 1] configuration at the next neighbored lattice site.
The transition involves the C$_{\text{i}}$ BC configuration, which, however, was found to be unstable relaxing into the C$_{\text{i}}$ \hkl<1 1 0> DB configuration.
-If the migration is considered to occur within a single step the kinetic energy of \unit[2.2]{eV} is enough to turn the \hkl<1 0 0> DB into the BC and back into a \hkl<1 0 0> DB configuration.
-If, on the other hand, a two step process is assumed the BC configuration will most probably relax into the C$_{\text{i}}$ \hkl<1 1 0> DB configuration resulting in different relative energies of the intermediate state and the saddle point.
-For the latter case a migration path, which involves a C$_{\text{i}}$ \hkl<1 1 0> DB configuration is proposed and displayed in Fig.~\ref{fig:mig}.
+If the migration is considered to occur within a single step, the kinetic energy of \unit[2.2]{eV} is enough to turn the \hkl<1 0 0> DB into the BC and back into a \hkl<1 0 0> DB configuration.
+If, on the other hand, a two step process is assumed, the BC configuration will most probably relax into the C$_{\text{i}}$ \hkl<1 1 0> DB configuration resulting in different relative energies of the intermediate state and the saddle point.
+For the latter case a migration path, which involves a C$_{\text{i}}$ \hkl<1 1 0> DB configuration, is proposed and displayed in Fig.~\ref{fig:mig}.
\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth]{110mig.ps}
Approximately \unit[2.24]{eV} are needed to turn the C$_{\text{i}}$ \hkl[0 0 -1] DB into the C$_{\text{i}}$ \hkl[1 1 0] DB located at the next neighbored lattice site in \hkl[1 1 -1] direction.
Another barrier of \unit[0.90]{eV} exists for the rotation into the C$_{\text{i}}$ \hkl[0 -1 0] DB configuration.
Roughly the same amount would be necessary to excite the C$_{\text{i}}$ \hkl[1 1 0] DB to the BC configuration (\unit[0.40]{eV}) and a successive migration into the \hkl[0 0 1] DB configuration (\unit[0.50]{eV}) as displayed in our previous study\cite{zirkelbach10a}.
-The former diffusion process, however, would more nicely agree to the ab initio path, since the migration is accompanied by a rotation of the DB orientation.
+The former diffusion process, however, would more nicely agree with the ab initio path, since the migration is accompanied by a rotation of the DB orientation.
By considering a two step process and assuming equal preexponential factors for both diffusion steps, the probability of the total diffusion event is given by $\exp(\frac{\unit[2.24]{eV}+\unit[0.90]{eV}}{k_{\text{B}}T})$, which corresponds to a single diffusion barrier that is 3.5 times higher than the barrier obtained by ab initio calculations.
-Accordingly the effective barrier of migration of C$_{\text{i}}$ is overestimated by a factor of 2.4 to 3.5 compared to the highly accurate quantum-mechanical methods.
+Accordingly, the effective barrier of migration of C$_{\text{i}}$ is overestimated by a factor of 2.4 to 3.5 compared to the highly accurate quantum-mechanical methods.
This constitutes a serious limitation that has to be taken into account for modeling the C-Si system using the EA potential.
\subsection{Molecular dynamics simulations}
By comparing the Si-C peaks of the low concentration simulation with the resulting Si-C distances of a C$_{\text{i}}$ \hkl<1 0 0> DB it becomes evident that the structure is clearly dominated by this kind of defect.
One exceptional peak exists, which is due to the Si-C cut-off, at which the interaction is pushed to zero.
Investigating the C-C peak at \unit[0.31]{nm}, which is also available for low C concentrations as can be seen in the inset, reveals a structure of two concatenated, differently oriented C$_{\text{i}}$ \hkl<1 0 0> DBs to be responsible for this distance.
-Additionally the Si-Si radial distribution shows non-zero values at distances around \unit[0.3]{nm}, which, again, is due to the DB structure stretching two next neighbored Si atoms.
+Additionally, the Si-Si radial distribution shows non-zero values at distances around \unit[0.3]{nm}, which, again, is due to the DB structure stretching two next neighbored Si atoms.
This is accompanied by a reduction of the number of bonds at regular Si distances of c-Si.
A more detailed description of the resulting C-Si distances in the C$_{\text{i}}$ \hkl<1 0 0> DB configuration and the influence of the defect on the structure is available in a previous study\cite{zirkelbach09}.
-For high C concentrations the defect concentration is likewise increased and a considerable amount of damage is introduced in the insertion volume.
+For high C concentrations, the defect concentration is likewise increased and a considerable amount of damage is introduced in the insertion volume.
A subsequent superposition of defects generates new displacement arrangements for the C-C as well as Si-C pair distances, which become hard to categorize and trace and obviously lead to a broader distribution.
-Short range order indeed is observed, i.e. the large amount of strong next neighbored C-C bonds at \unit[0.15]{nm} as expected in graphite or diamond and Si-C bonds at \unit[0.19]{nm} as expected in SiC, but only hardly visible is the long range order.
+Short range order indeed is observed, i.e. the large amount of strong next neighbored C-C bonds at \unit[0.15]{nm} as expected in graphite or diamond and Si-C bonds at \unit[0.19]{nm} as expected in SiC, but hardly visible is the long range order.
This indicates the formation of an amorphous SiC-like phase.
-In fact resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential\cite{gao02}.
+In fact, resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential\cite{gao02}.
In both cases, i.e. low and high C concentrations, the formation of 3C-SiC fails to appear.
-With respect to the precipitation model the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs indeed occurs for low C concentrations.
+With respect to the precipitation model, the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs indeed occurs for low C concentrations.
However, sufficient defect agglomeration is not observed.
-For high C concentrations a rearrangement of the amorphous SiC structure, which is not expected at prevailing temperatures, and a transition into 3C-SiC is not observed either.
+For high C concentrations, a rearrangement of the amorphous SiC structure, which is not expected at prevailing temperatures, and a transition into 3C-SiC is not observed either.
On closer inspection two reasons for describing this obstacle become evident.
-First of all there is the time scale problem inherent to MD in general.
+First of all, there is the time scale problem inherent to MD in general.
To minimize the integration error the discretized time step must be chosen smaller than the reciprocal of the fastest vibrational mode resulting in a time step of \unit[1]{fs} for the investigated materials system.
Limitations in computer power result in a slow propagation in phase space.
Several local minima exist, which are separated by large energy barriers.
-Due to the low probability of escaping such a local minimum a single transition event corresponds to a multiple of vibrational periods.
-Long-term evolution such as a phase transformation and defect diffusion, in turn, are made up of a multiple of these infrequent transition events.
+Due to the low probability of escaping such a local minimum, a single transition event corresponds to a multiple of vibrational periods.
+Long-term evolution, such as a phase transformation and defect diffusion, in turn, are made up of a multiple of these infrequent transition events.
Thus, time scales to observe long-term evolution are not accessible by traditional MD.
New accelerated methods have been developed to bypass the time scale problem retaining proper thermodynamic sampling\cite{voter97,voter97_2,voter98,sorensen2000,wu99}.
-However, the applied potential comes up with an additional limitation already mentioned in the introductory part.
+However, the applied potential comes up with an additional limitation, as previously mentioned in the introduction.
The cut-off function of the short range potential limits the interaction to next neighbors, which results in overestimated and unphysical high forces between next neighbor atoms.
This behavior, as observed and discussed for the Tersoff potential\cite{tang95,mattoni2007}, is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:cmob}.
-Indeed it is not only the strong C-C bond which is hard to break inhibiting C diffusion and further rearrangements in the case of the high C concentration simulations.
+Indeed, it is not only the strong, hard to break C-C bond inhibiting C diffusion and further rearrangements in the case of the high C concentration simulations.
This is also true for the low concentration simulations dominated by the occurrence of C$_{\text{i}}$ \hkl<1 0 0> DBs spread over the whole simulation volume, which are unable to agglomerate due to the high migration barrier.
\subsection{Increased temperature simulations}
-Due to the potential enhanced problem of slow phase space propagation, pushing the time scale to the limits of computational resources or applying one of the above mentioned accelerated dynamics methods exclusively might not be sufficient.
-Instead higher temperatures are utilized to compensate overestimated diffusion barriers.
+Due to the problem of slow phase space propagation, which is enhanced by the employed potential, pushing the time scale to the limits of computational resources or applying one of the above mentioned accelerated dynamics methods exclusively might not be sufficient.
+Instead, higher temperatures are utilized to compensate overestimated diffusion barriers.
These are overestimated by a factor of 2.4 to 3.5.
Scaling the absolute temperatures accordingly results in maximum temperatures of \unit[1460-2260]{$^{\circ}$C}.
Since melting already occurs shortly below the melting point of the potential (2450 K)\cite{albe_sic_pot} due to the presence of defects, a maximum temperature of \unit[2050]{$^{\circ}$C} is used.
\label{fig:tot}
\end{figure}
The first noticeable and promising change observed for the Si-C bonds is the successive decline of the artificial peak at the cut-off distance with increasing temperature.
-Obviously enough kinetic energy is provided to affected atoms that are enabled to escape the cut-off region.
-Additionally a more important structural change was observed, which is illustrated in the two shaded areas of the graph.
-Obviously the structure obtained at \unit[450]{$^{\circ}$C}, which was found to be dominated by C$_{\text{i}}$, transforms into a C$_{\text{s}}$ dominated structure with increasing temperature.
-Comparing the radial distribution at \unit[2050]{$^{\circ}$C} to the resulting bonds of C$_{\text{s}}$ in c-Si excludes all possibility of doubt.
+Obviously, sufficient kinetic energy is provided to affected atoms that are enabled to escape the cut-off region.
+Additionally, a more important structural change was observed, which is illustrated in the two shaded areas of the graph.
+Obviously, the structure obtained at \unit[450]{$^{\circ}$C}, which was found to be dominated by C$_{\text{i}}$, transforms into a C$_{\text{s}}$ dominated structure with increasing temperature.
+Comparing the radial distribution at \unit[2050]{$^{\circ}$C} to the resulting bonds of C$_{\text{s}}$ in c-Si excludes any possibility of doubt.
The phase transformation is accompanied by an arising Si-Si peak at \unit[0.325]{nm}, which corresponds to the distance of second next neighbored Si atoms along \hkl<1 1 0> bond chain with C$_{\text{s}}$ in between.
Since the expected distance of these Si pairs in 3C-SiC is \unit[0.308]{nm} the existing SiC structures embedded in the c-Si host are stretched.
-According to the C-C radial distribution agglomeration of C fails to appear even for elevated temperatures as can be seen on the total amount of C pairs within the investigated separation range, which does not change significantly.
+According to the C-C radial distribution, agglomeration of C fails to appear even for elevated temperatures, as can be seen on the total amount of C pairs within the investigated separation range, which does not change significantly.
However, a small decrease in the amount of next neighbored C pairs can be observed with increasing temperature.
This high temperature behavior is promising since breaking of these diamond- and graphite-like bonds is mandatory for the formation of 3C-SiC.
-Obviously acceleration of the dynamics occurred by supplying additional kinetic energy.
+Obviously, acceleration of the dynamics occurred by supplying additional kinetic energy.
A slight shift towards higher distances can be observed for the maximum located shortly above \unit[0.3]{nm}.
Arrows with dashed lines mark C-C distances resulting from C$_{\text{i}}$ \hkl<1 0 0> DB combinations while arrows with solid lines mark distances arising from combinations of C$_{\text{s}}$.
The continuous dashed line corresponds to the distance of C$_{\text{s}}$ and a next neighbored C$_{\text{i}}$ DB.
-Obviously the shift of the peak is caused by the advancing transformation of the C$_{\text{i}}$ DB into the C$_{\text{s}}$ defect.
+Obviously, the shift of the peak is caused by the advancing transformation of the C$_{\text{i}}$ DB into the C$_{\text{s}}$ defect.
Quite high g(r) values are obtained for distances in between the continuous dashed line and the first arrow with a solid line.
For the most part these structures can be identified as configurations of C$_{\text{s}}$ with either another C atom that basically occupies a Si lattice site but is displaced by a Si interstitial residing in the very next surrounding or a C atom that nearly occupies a Si lattice site forming a defect other than the \hkl<1 0 0>-type with the Si atom.
Again, this is a quite promising result since the C atoms are taking the appropriate coordination as expected in 3C-SiC.
No significant change in structure is observed.
However, the decrease of the cut-off artifact and slightly sharper peaks observed with increasing temperature, in turn, indicate a slight acceleration of the dynamics realized by the supply of kinetic energy.
However, it is not sufficient to enable the amorphous to crystalline transition.
-In contrast, even though next neighbored C bonds could be partially dissolved in the system exhibiting low C concentrations the amount of next neighbored C pairs even increased in the latter case.
-Moreover the C-C peak at \unit[0.252]{nm}, which gets slightly more distinct, equals the second next neighbor distance in diamond and indeed is made up by a structure of two C atoms interconnected by a third C atom.
-Obviously processes that appear to be non-conducive are likewise accelerated in a system, in which high amounts of C are incorporated within a short period of time, which is accompanied by a concurrent introduction of accumulating, for the reason of time non-degradable, damage.
+In contrast, even though next neighbored C bonds could be partially dissolved in the system exhibiting low C concentrations, the amount of next neighbored C pairs even increased in the latter case.
+Moreover, the C-C peak at \unit[0.252]{nm}, which gets slightly more distinct, equals the second next neighbor distance in diamond and indeed is made up by a structure of two C atoms interconnected by a third C atom.
+Obviously, processes that appear to be non-conducive are likewise accelerated in a system, in which high amounts of C are incorporated within a short period of time, which is accompanied by a concurrent introduction of accumulating, for the reason of time non-degradable damage.
% non-degradable, non-regenerative, non-recoverable
Thus, for these systems even larger time scales, which are not accessible within traditional MD, must be assumed for an amorphous to crystalline transition or structural evolution in general.
% maybe put description of bonds in here ...
Nevertheless, some results likewise indicate the acceleration of other processes that, again, involve C$_{\text{s}}$.
The increasingly pronounced Si-C peak at \unit[0.35]{nm} corresponds to the distance of a C and a Si atom interconnected by another Si atom.
-Additionally the C-C peak at \unit[0.31]{nm} corresponds to the distance of two C atoms bound to a central Si atom.
+Additionally, the C-C peak at \unit[0.31]{nm} corresponds to the distance of two C atoms bound to a central Si atom.
For both structures the C atom appears to reside on a substitutional rather than an interstitial lattice site.
-However, huge amount of damage hampers identification.
+However, huge amounts of damage hampers identification.
The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necessity of much more time for structural evolution to maintain the topotactic orientation of the precipitate.
\section{Summary and discussion}
In a previous comparative study\cite{zirkelbach10a} we have shown that the utilized empirical potential fails to describe some selected processes.
Thus, limitations of the employed potential have been further investigated and taken into account in the present study.
We focussed on two major shortcomings: the overestimated activation energy and the improper description of intrinsic and C point defects in Si.
-Overestimated forces between next neighbor atoms that are expected for short range potentials\cite{mattoni2007} have been confirmed to influence the C$_{\text{i}}$ diffusion.
+Overestimated forces between nearest neighbor atoms that are expected for short range potentials\cite{mattoni2007} have been confirmed to influence the C$_{\text{i}}$ diffusion.
The migration barrier was estimated to be larger by a factor of 2.4 to 3.5 compared to highly accurate quantum-mechanical calculations\cite{zirkelbach10a}.
-Concerning point defects the drastically underestimated formation energy of C$_{\text{s}}$ and deficiency in the description of the Si$_{\text{i}}$ ground state necessitated further investigations on structures that are considered important for the problem under study.
+Concerning point defects, the drastically underestimated formation energy of C$_{\text{s}}$ and deficiency in the description of the Si$_{\text{i}}$ ground state necessitated further investigations on structures that are considered important for the problem under study.
It turned out that the EA potential still favors a C$_{\text{i}}$ \hkl<1 0 0> DB over a C$_{\text{s}}$-Si$_{\text{i}}$ configuration, which, thus, does not constitute any limitation for the simulations aiming to resolve the present controversy of the proposed SiC precipitation models.
MD simulations at temperatures used in IBS resulted in structures that were dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume.
Incorporation into volumes $V_2$ and $V_3$ led to an amorphous SiC-like structure within the respective volume.
-To compensate overestimated diffusion barriers we performed simulations at accordingly increased temperatures.
+To compensate overestimated diffusion barriers, we performed simulations at accordingly increased temperatures.
No significant change was observed for high C concentrations.
The amorphous phase is maintained.
Due to the incorporation of a huge amount of C into a small volume within a short period of time damage is produced, which obviously decelerates structural evolution.
% postannealing less efficient than hot implantation
Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates\cite{eichhorn02}.
-In particular restructuring of strong C-C bonds is affected\cite{deguchi92}, which preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
+In particular, restructuring of strong C-C bonds is affected\cite{deguchi92}, which preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
We assume this to be related to the problem of slow structural evolution encountered in the high C concentration simulations due to the insertion of high amounts of C into a small volume within a short period of time resulting in essentially no time for the system to rearrange.
% rt implantation + annealing
Implantations of an understoichiometric dose at room temperature followed by thermal annealing results in small spherical sized C$_{\text{i}}$ agglomerates at temperatures below \unit[700]{$^{\circ}$C} and SiC precipitates of the same size at temperatures above \unit[700]{$^{\circ}$C}\cite{werner96}.
Since, however, the implantation temperature is considered more efficient than the postannealing temperature, SiC precipitates are expected -- and indeed are observed for as-implanted samples\cite{lindner99,lindner01} -- in implantations performed at \unit[450]{$^{\circ}$C}.
-Implanted C is therefor expected to occupy substitutionally usual Si lattice sites right from the start.
+Implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
Thus, we propose an increased participation of C$_{\text{s}}$ already in the initial stages of the implantation process at temperatures above \unit[450]{$^{\circ}$C}, the temperature most applicable for the formation of SiC layers of high crystalline quality and topotactical alignment\cite{lindner99}.
Thermally activated, C$_{\text{i}}$ is enabled to turn into C$_{\text{s}}$ accompanied by Si$_{\text{i}}$.
The associated emission of Si$_{\text{i}}$ is needed for several reasons.
-For the agglomeration and rearrangement of C Si$_{\text{i}}$ is needed to turn C$_{\text{s}}$ into highly mobile C$_{\text{i}}$ again.
-Since the conversion of a coherent SiC structure, i.e. C$_{\text{s}}$ occupying the Si lattice sites of one of the two fcc lattices that build up the c-Si diamond lattice, into incoherent SiC is accompanied by a reduction in volume, large amount of strain is assumed to reside in the coherent as well as incoherent structure.
-Si$_{\text{i}}$ serves either as supply of Si atoms needed in the surrounding of the contracted precipitates or as interstitial defect minimizing the emerging strain energy of a coherent precipitate.
+For the agglomeration and rearrangement of C, Si$_{\text{i}}$ is needed to turn C$_{\text{s}}$ into highly mobile C$_{\text{i}}$ again.
+Since the conversion of a coherent SiC structure, i.e. C$_{\text{s}}$ occupying the Si lattice sites of one of the two fcc lattices that build up the c-Si diamond lattice, into incoherent SiC is accompanied by a reduction in volume, large amounts of strain are assumed to reside in the coherent as well as at the surface of the incoherent structure.
+Si$_{\text{i}}$ serves either as a supply of Si atoms needed in the surrounding of the contracted precipitates or as an interstitial defect minimizing the emerging strain energy of a coherent precipitate.
The latter has been directly identified in the present simulation study, i.e. structures of two C$_{\text{s}}$ atoms with one being slightly displaced by a next neighbored Si$_{\text{i}}$ atom.
It is, thus, concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.\cite{nejim95}.
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\section*{Acknowledgment}
We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (DPA-61/05) and the Deutsche Forschungsgemeinschaft (DFG SCHM 1361/11).
+Meta Schnell is greatly acknowledged for a critical revision of the present manuscript.
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